In this lab we will be comparing the results from a three-phase circuit and the results from an equivalent single-phase

circuit. The power factor of the threephase system will be adjusted by proper placement of a shunt capacitor. We will familiarize ourselves with the Simulink library. Procedure a. The three-phase circuit from lab1 was modified and edited by adding new components to the circuit. b. From the Simulink library the circuit was modified appreciably by replacing some various elements to suit the elements for lab2. c. The waveforms of Van and ia1-b1 were plotted on the same graph with the help of the Mux and the Scope tools from the Simulink library. d. The three-phase circuit was modified and an equivalent singlephase circuit was obtained. And Van and Va1-n1 were calculated and plotted on the same graph with the aid of the same components as before. e. Further on, the waveforms of ia1-b1 and Va1-b1 were obtained from the three-phase circuit from the lab manual. f. in-n1 was obtained for every Rn =0.5, 1.0 and 10.0 and was plotted g. The La1n1 were adjusted to j10 and the above procedure was repeated again but his time with only Rn=0.5 and 10. h. The various powers were obtained by multiplying the current and voltages in each branch. i. The inductors in the second branch were replaced with capacitors, with the purpose of reducing the power dissipation in the circuit. j. After the capacitors were replaced the powers were calculated again. Results The circuit equivalent using from the lab manual using the Simpower tool kit is shown below.

The waveform of both Van and ia1-b1 on the same figure is as shown below.

The figures as follows depict the waveform of Van and V1a-1n and the equivalent circuit of the single-phase circuit of the three-phase circuit.

When Rn=0.5 the in-1n waveform was obtained as follows in the figure below and basically the figure showed there was no current flowing the Rn the current was very close to zero.

At Rn=1 the following figure shows the changes in the above figures for in-n1. The waveform was a bit noisy and followed the same reason, as Rn was .5.

The Rn was adjusted to 10 and the screenshot of the waveform was taken and is as shown below. There was a lot of noise when Rn was increased.

Ln1 was changed to j10 and Rn=.5 and the simulation was ran again and the figure below was obtained and it could be verified from the previous waveform when Rn=0.5. Changing Ln1 acted like a filter, which got rid of all the noise in the wave form.

Ln1 was kept at j10 and the Rn varied to 10, there were no big difference between the above waveform and the waveform below rather the amplitude was influenced a lot.

The phasor total power dissipation from the three-phase circuit

The three-phase circuit was adjusted by replacing the resistors with capacitors in the second branch. And the total power dissipation was calculated again in the waveform representation.

Conclusion This lab enriched our understanding of the equivalent representation of a single-phase circuit of the three-phase circuit. It was verified that changing the value of Rn had a very little influence of the circuit. Which was tested by finding the current through the Rn and it was verified that the current through the Rn was though not zero but very close to zero. The power dissipation in the circuit were able to be altered when the resistances were replaced with capacitors in the threephase circuit. We familiarized ourselves with the Powersim tool kit in Matlab.